From this blog:https://web.archive.org/web/20150427230456/samuraimoon.blog67.fc2.com/blog-entry-226.html
(うわ、こいつストーカー? センター試験から目を付けられてたわけ!? 月くん貞操のぴんちっ!)とか思っている目ですが、おくびにも出さずに会話を続けます。
Context: It's from a scene in death note were L starts talking to Light out of the blue when they first met, here Light thinks to himsef "why is this weird guy (who's staring at me all the time) talking to me?"
I find this part very difficult to understand because I'm not sure who is saying this. At first I thought It could be Light because that part (うわ、こいつストーカー? センター試験から目を付けられてたわけ!? 月くん貞操のぴんちっ!) is in blue in the post and that's the color the author uses for all of Light's speeches so far. Also I think he uses sentences in () for when the characters are thinking to themselves; but Light would be referring to himself as 月くん in his thoughts which I don't think that's possible, that's why I was thinking that line was from the author.
For the meaning of 思っている目 I think it's something like: Eyes that seem to be thinking of (something) like in "someone has a look in his eyes that he is thinking of ...". But maybe 目 doesn't mean literal eyes, maybe it means viewpoint or attitude in this context.
I found this sentence too (which is clear that 目 means literal eyes):
メガネをすることでそのコンプレックスと思っている目を隠すことができるのです。
I guess this would be: Eyes that seem to be thinking of inferiority complex = Eyes that make one think of inferiority complex